\[t,\ ч\] | \[V,\ \frac{км}{ч}\] | \[S,\ км\] | |
---|---|---|---|
\[По\ расписанию\] |
\[\frac{80}{x}\] \[на\ 16\ мин > \searrow\] |
\[x\] | |
\[Нажал\ опоздание\] | \[\frac{80}{x + 10}\] | \[x + 10\] |
\[Составим\ уравнение:\]
\[\frac{80}{x} - \frac{80}{x + 10} = \frac{4}{15}\]
\[\frac{80 \cdot (x + 10) - 80x}{x(x + 10)} = \frac{4}{15}\]
\[\frac{80x + 800 - 80x}{x(x + 10)} = \frac{4}{15}\]
\[15 \cdot 800 = 4x^{2} + 40x\]
\[4x² + 40x - 12000 = 0\ \ \ |\ :4\]
\[x^{2} + 10x - 3000 = 0\]
\[D = b^{2} - 4ac = 100 - 4 \cdot ( - 3000) =\]
\[= 100 + 12000 = 12100\]
\[x_{1} = \frac{- 10 + 110}{2} = \frac{100}{2} = 50\]
\[x_{2} = \frac{- 10 - 110}{2} = - \frac{120}{2} = - 60 < 0 \Longrightarrow\]
\[\Longrightarrow не\ подходит.\]
\[Ответ:по\ расписанию\ скорость\ поезда\ \]
\[составляет\ 50\ \frac{км}{ч}.\]
\[y = \frac{6 - x}{5} - 2\]
\[\frac{6 - x}{5} - 2 < 0\]
\[\frac{6 - x - 10}{5} < 5\]
\[\frac{- 4 - x}{5} < 0\]
\[- 4 - x < 0\]
\[- x < 4\]
\[x > - 4\]
\[Ответ:x \in ( - 4;\ + \infty).\]
\[4 \cdot (2x - 1) - 3 \cdot (3x + 2) > 1\]
\[8x - 4 - 9x - 6 > 1\]
\[- x > 1 + 10\]
\[- x > 11\]
\[x < - 11\]
\[\mathbf{Ответ:}x \in ( - \infty; - 11).\]
\[\left( \sqrt{15} + \sqrt{5} \right) \cdot \sqrt{15} - \frac{5}{3}\sqrt{27} =\]
\[= 15 + 5\sqrt{3} - \frac{5}{3} \cdot 3\sqrt{3} =\]
\[= 15 + 5\sqrt{3} - 5\sqrt{3} = 15\]
\[\left( \frac{3}{9 - x^{2}} + \frac{1}{x - 3} \right)\ :\frac{x}{x^{2} - 6x + 9} =\]
\[= \left( - \frac{3}{x^{2} - 9} + \frac{1}{x - 3} \right)\ :\frac{x}{(x - 3)^{2}} =\]
\[= \frac{- 3 + (x + 3) \cdot (x - 3)^{2}}{\left( x^{2} - 9 \right) \cdot x} =\]
\[= \frac{x(x - 3)(x - 3)}{(x - 3)(x + 3) \cdot x} = \frac{x - 3}{x + 3}\]